Magic/calculations
Based on the information from Magic#Costs of mages. Based on that we might need to make a calculator (when the investments pay off?). Take into account, we don't have the formula of hired-mage increase, so the calculator could only give some approximate time then (if created). Plan A. First hire 1 mage; then 1/3/6 to catch up Maths of Upgrading Mages. Two projects. Before. VARIABLES - budget = 50k - main mage: shards per hour = 66 - main mage: % chance to get 2x shards = 8% - shard per hour upgrade cost = 5.7k - hiring mage: cost per hour1 = 730 (at 66 + 8%) *- hiring mage: cost per hour2 = 734 (if upgraded 66->67 + 8%) COUNTING VARIABLES: NOW (if 66 + 8%) 1) - hiring mage: shards per hour1 = 66/2 = 33 2) - hiring mage: % chance to get 2x shards1 = 8%/2 = 4% 3) - main mage: shards per hour, adjusted on %-chance1 = 66*2*8% + 66*1*(100%−8%) = 71.28 4) - hiring mage: shards per hour, adjusted on %-chance1 = 33*2*4% + 33*1*(100%−4%) = 34.32 NEW (if 67 + 8%) 1) - hiring mage: shards per hour2 = 67/2 = 33.5 {it is now correct, because it will be floored to 33, but whatever} 2) - hiring mage: % chance to get 2x shards2 = 8%/2 = 4% 3) - main mage: shards per hour, adjusted on %-chance2 = 67*2*8% + 67*1*(100%−8%) = 72.36 4) - hiring mage: shards per hour, adjusted on %-chance2 = 33.5*2*4% + 33.5*1*(100%−4%) = 34.84 Project 1. Invest in one mage (50k). Project 2. Buy one upgrade (5.7k). Invest in one mage the rest (50k − 5.7k). {Tip: Hiring one or seven mages will give the same amount of shards} {Tip: Though the mefail's calculators says that there is difference. Hm. If it because of flooring?) Calculations. Project 1. Hours_hiring_mage_works1 = 50k / 730 = 68.5 hours (with 34.32 shards per hour, adjusted). Total_hiring_mage_makes1 = 68.5*34.32 = 2350.92 Total_main_mage_will_make1 = 71.28*68.5 = 4882.68 SubSubtotal1 = 2350.92 + 4882.68 = 7233.6 (in 68.5 hours) Project 2. Hours_hiring_mage_works2 = (50k−5.7k) / 734 = 60.35 hours (with 34.84 shards per hour, adjusted). Total_hiring_mage_makes2 = 60.35*34.84 = 2102.59 //Hours_that_main_mage_will_be_alone = 68.5 − 60.35 = 8.15 Total_main_mage_will_make2 = 72.36*68.5 = 4956.66 {Tip: to harmonize the time, we took the main mage time as constant, 68.5. So if project 2 main mage will work alone for a long time} SubSubtotal2 = 2102.59 + 4956.66 = 7059.25 (in 68.5 hours) SUBTOTAL All hired mages dissapeared. 7059.25 − 7233.6 = (−174.35) shards lost in 68.5 hours. {How many time do we need to recover those 174.35 with a new efficiency? That is when the number of mages matter} With no hired mages: 174.35 / (72.36 − 71.28) = 161.44 (7 days) With three hired mages: 174.35 / ((72.36 − 71.28) + 3*(34.84 − 34.32)) = 66.04 (3 days) With all (six) hired mages 174.35 / ((72.36 − 71.28) + 6*(34.84 − 34.32)) = 41.51 (2 days) Plan B. First hire 6 (all) mages; then 1/3/6 to catch up Maths of Upgrading Mages. Two projects.